Logical Expressiveness of Graph Neural Networks with Hierarchical Node Individualization
By: Arie Soeteman, Balder ten Cate
Potential Business Impact:
Helps computers understand complex connections better.
We propose and study Hierarchical Ego Graph Neural Networks (HEGNNs), an expressive extension of graph neural networks (GNNs) with hierarchical node individualization, inspired by the Individualization-Refinement paradigm for graph isomorphism testing. HEGNNs generalize subgraph-GNNs and form a hierarchy of increasingly expressive models that, in the limit, can distinguish graphs up to isomorphism. We provide a logical characterization of HEGNN node classifiers, with and without subgraph restrictions, using graded hybrid logic. This characterization enables us to relate the separating power of HEGNNs to that of higher-order GNNs, GNNs enriched with local homomorphism count features, and color refinement algorithms based on Individualization-Refinement. Our experimental results confirm the practical feasibility of HEGNNs and show benefits in comparison with traditional GNN architectures, both with and without local homomorphism count features.
Similar Papers
Multi-Granular Attention based Heterogeneous Hypergraph Neural Network
Machine Learning (CS)
Finds hidden connections in complex data.
Implicit Hypergraph Neural Networks: A Stable Framework for Higher-Order Relational Learning with Provable Guarantees
Machine Learning (CS)
Helps computers understand group connections better.
Are Heterogeneous Graph Neural Networks Truly Effective? A Causal Perspective
Machine Learning (CS)
Makes computers understand complex connections better.